I do pullups and chinups in my garage all the time. I do them on a metal beam that runs across the ceiling and helps hold up the second floor. It is an I beam, so my grip isn't ever really ideal, but I don't have a problem with it.
If I were to use a more conventional bar, would the amount of reps I can do increase?
Just curious.
Yes, having a better grip makes pull-ups a lot easier, and increases the number you can do, often dramatically.
Gripping tight would also create tension in your body, which helps for exciting the CNS. Here is a link: http://www.rdlfitness.com/use-a-tight-grip/
It would get your grip stronger, it would increase your pull-up power.
